Marko Malink is Assistant Professor of Philosophy at the University of Chicago. Click here to listen to our conversation with him.

An episode on modal syllogistic is guaranteed to sound a bit challenging to someone who hasn’t ever studied logic. But the topic isn’t just fascinating–it’s easy to grasp once you’ve learned some of the relevant terminology. If you’ve never taken an introductory course in logic before, I recommend taking a look at my entry from earlier this year at the Partially Examined Life blog, which introduces some of the basic concepts in philosophical logic.

Our discussion with Marko Malink turns on the meaning of words that philosophers and linguists call quantifiers. Quantifiers are the words we use to make generalizations, including every, some, all, no, most, few, and many.

At the beginning of the 20th century, philosopher and mathematician Gottlob Frege revolutionized logic by offering a new definition of the quantifiers all, every and some. We say things like ‘all French people love Jerry Lewis’ on a daily basis, but of course that doesn’t mean we’ve thought about how to define them precisely. Luckily, Frege did it for us. He would have thought that ‘all French people love Jerry Lewis’ meant ‘for everything, if that thing is a French person, then it loves Jerry Lewis.’

As Marko Malink points out, this defnition has a specific consequence: namely, it makes the truth or falsity of sentences like ‘all Xs are Y’ depend on nothing more than what falls into the category X and what falls into the category Y. (Philosophers call sentences whose truth or falsity depends only on what falls into what category extensional sentences.) In other words, if you want to figure out whether ‘all Xs are Y’ is true, you just go around checking to see whether every X happens to be Y. Take a list of all the Xs, and write a check mark next to each one if you find that it’s Y. If every item in your list ends up with a check mark next to it, then it’s true that all Xs are Y. Another way to put the idea is in terms of sets. If you say ‘all Xs are Y,’ then you’re saying that the set of Xs is a subset of the set of Ys.

This turned out to be an immensely useful way to understand statements like ‘all Xs are Y,’ and remains central to the way we think about them today. But according to Marko Malink, Aristotle was working under a different definition. Unfortunately, Aristotle never states the precise definition he’s using, so we don’t know exactly what statements like ‘all French people love Jerry Lewis’ would have meant, from his point of view. However, as Malink points out, we do know that he wouldn’t have thought of them as extensional–as depending for their truth and falsity only on what falls into what category.

How do we know that? Well, Aristotle draws a distinction between two kinds of properties: substance properties and accidental properties. (In ancient Greek philosophy, ‘substance’ didn’t necessarily mean physical matter, the way it usually does today. For the purposes of this discussion, think of it as a technical term meaning ‘real, existing thing.’) Bearing a substance property means being one kind of thing rather than another: for instance, being a giraffe, or a horse, or a person. Bearing an accidental property means having some random feature rather than another–a random feature that anything could have, in principle. Like being brown or green. What’s the difference between kinds of things and features of things? Something like this: if you tell me that something is this sort of substance rather than that sort of substance, you’ve really told me something informative about it. But if you tell me that something has some old random feature, you haven’t really given me any special insight into it.

Suppose I perceived the vague outline of an animal off in the distance, then asked: ‘What is that thing?’ If you replied, ‘It’s a giraffe,’ there’s the sense that you would be giving me significant information about the nature of the animal I was looking at. ‘Ah yes; a giraffe,’ I would say. But if you replied, ‘It’s something brown,’ there’s the sense that you wouldn’t have really told me anything informative about what I was looking at. That’s part of why I would never respond by saying, ‘Ah yes; a brown thing.’

Malink argues that the difference between the Fregean definition of quantifiers like ‘all’ and the Aristotelian definition of quantifiers like ‘all’ is this. According to Frege’s definition, it doesn’t really matter what properties X and Y are when you say ‘all Xs are Y.’ As long as the Xs are a subset of the Ys, the sentence is true. But according to Aristotle’s definition, ‘all Xs are Y’ can’t be true when X is an accidental property and Y is a substance property. It can only be true when both X and Y are substance properties, or when X is a substance property and Y is an accidental property.

Here’s an example. All mandrills (more or less) have blue and red ridged noses. And it so happens that they’re the only animal with noses like that. So under Frege’s definition of ‘all,’ both of these sentences are true:

(1) All mandrills have blue and red ridged noses.
(2) All possessors of blue and red ridged noses are mandrills.

Why? Well, since the set of mandrills and the set of blue and red ridged nose possessors have the same members, they’re the same set, and thus they’re subsets of each other. Therefore, both (1) and (2) are true. But under Aristotle’s definition–whatever that definition may have been–only (1) can be true, because (2) tries to ascribe a substance property (being a mandrill) to everything that has an accidental property (having a blue and red ridged nose). In Aristotle’s view, you only get to make general claims about anything that has a substance property.

Marko Malink goes on to claim that this fact about Aristotle’s basic logical framework is crucial for understanding how his more sophisticated logical framework–which we call modal syllogistic–works. In our next post, we’ll discuss why.

3 Responses

Very interesting podcast and discussion, Matt. I’m pleased to see giraffes becoming a standard example across the philosophy podcasting world!

A couple of thoughts about extensionality and Aristotelian logic: I think there’s reasonably good evidence that Aristotle does think that part of the truth conditions for “All A are B” is that there be at least one A. Thus, there is what Prof Malink was calling (I think) “existential import” for such predications. This kind of makes sense: how could we know/how could it be true that all A are B if there aren’t any A things to be B? And I would also say that for him a universal predication is “made true” by the existence of individuals, this would be part of his rejection of Platonic Forms (we see it at work in his characterization in the Categories of individuals as primary substances).

That relates to another issue which is Aristotle’s epistemology: his theory of induction suggests that we do somehow get to universal predications on the basis of looking at individual instances. It’s an interesting question whether Aristotle keeps clearly apart, as we’d want him to, the issues of truth conditions and of epistemic access. In other words, he may be assuming that the truth conditions of a predication are intimately related to the possibility of knowing the predication to be true.

Peter: thanks! These are fascinating points, as always. I don’t have much to add, except for a tangential remark that’s related to my own area of research. I’ve talked to Marko Malink about the issue of induction a little, and it seems that one possible interpretation of universal statements in Aristotle is as what contemporary philosophers call ‘generic statements.’

Generic statements are loose generalizations: they hold for the most part, but can have the occasional exception here and there without that exception making them false. For example, most people would say that the statement ‘Birds fly’ is true, even though we all know that penguins are birds and that penguins don’t fly. There’s a huge discussion in philosophy and linguistics about how it’s possible for those three statements to be consistent. What are statements like ‘birds fly’ really saying?

Anyway, there’s a lot we could say about that, but let’s get back to Aristotle. One hypothesis that’s consistent with what Aristotle says is that for him, ‘Every A is B’ means something like ‘As are B’ (in the relevant sense of ‘birds fly,’ given above). Of course, this is only one possibility among many. But if it’s correct, then it fits nicely with the last two points you made. There’s some recent research at the border between psychology and philosophy which suggests that generic statements are the natural home for inductive reasoning in young children. Children only get good at reasoning with quantifiers starting at a later age.

So if Aristotle indeed meant ‘As are B’ by ‘Every A is B,’ then perhaps universal statements in syllogistic have even more of a claim to being the endpoint of inductive reasoning than universal statements in modern logic!

Re: giraffes, a number of people who listen to both Elucidations and The History of Philosophy Without Any Gaps have asked me whether the two of us have a mind meld. I’ve been using them as examples in papers, conversations, lectures, and grant applications for many years! But here’s a question: how did yours come to be named Hiawatha?

I am new to the set of those who have discovered Elucidations, a pleasant fact indeed. Please continue this stimulating broadcast.

The episode concerning modal syllogistic prompts these comments: as a lay person I found the discussion difficult to follow. While I intend to read further on the subject presented, please accept this initial remark; perhaps the discussion can benefit from structure enforced by the host(s). I draw your attention to the brilliant work of Alan Saunders with his Philosopher’s Zone. Saunders is expert at restating and at clarifying the statements of his guests, at establishing a priori the exposition of particularly opaque concepts.

Please understand, I intend as praise this comparison to Alan Saunders. I believe through conscious practice Elucidations can attain the brilliance of Philosopher’s Zone. I am eager to follow your successful maturation.